Joint Requirement of Two Multi-skill Resource Types in Multi-period Multi-site Assignment Problem

A classic assignment problem determines how to assign resources to tasks in the best possible way. Over the past years, the classic assignment problem has been extended and more complicated assignment models have been proposed. A multi-period multi-site assignment problem is one extension of the classic assignment problem. The number of sites and periods is increased to more than one and the decision is extended to consider assigning resources to site while concerning tasks in each site and period. Most multi-period multi-site assignment models do not concern joint resources for operation; however, in some real-life problems, there is a case in which joint resources for performing tasks are required. In this study, we consider joint requirement of two multi-skill resource types in the multi-period multi-site assignment problem and propose the mathematical model and a heuristic approach. The developed heuristic is comprised of two phases. An initial solution is generated by CPLEX in the first phase. Then the solution is improved in the second phase using proposed heuristic. This heuristic aims to allocate resources to better sites and assign resources to suitable tasks. In the computational experiment, the number of resources and the ratio of tasks requiring joint resources are varied. The result shows that the complexity of the problem highly depends on the ratio of task requiring joint resources. When all parameters are fixed except for the number of resources, there is only one range of the number of resources that makes the problem complex. For the efficiency of the algorithm, the developed heuristic can find good solutions in a short time in all ranges of the number of resources in all test problems, and optimal gaps slightly increase when the ratio of tasks requiring joint resources increases (average optimal gap of all test problems is 7.25%).